Research On Compressed Sensing For UWB Systems

Ultra-wideband (UWB) is a new technology for short-range wireless communications. In comparison with the conventional wireless communication technologies, UWB has many appealing advantages including high data rate, low cost, low-transmit power, and low interference. Therefor, it becomes a breakthrough for wireless communications. However, according to the Nyquist sampling theory, extremely high sampling rates are required by UWB receivers to realize digital signal processing. Due to the fact that the "state of the art" of high speed analog-to-digital converters (ADCs) cannot meet the urgent requirements especially in terms of sampling speed and cost, the sampling of UWB signals is evidently one of the bottleneck restrictions in the development of UWB systems.Compressed Sensing (CS) theory, which is proposed in2004, gives a way to resolve the above-mentioned UWB sampling problem. As reported in the literature, UWB signals show remarkable sparsity. According to the CS theory, sparse signals can be sampled by using sampling rates much lower than Nyquist Rate. Meanwhile, the original signals can be recovered or approximated with high probability by using specified reconstruction algorithms. Evidently, CS is a good choice for UWB systems to bypass the dependence on high speed ADCs. In this thesis, taking the characteristics of UWB signals and the constraints imposed by the UWB receivers into consideration, we mainly focus on two technical aspects relevant to CS, i.e., measurement matrix and redundant dictionary. The main contributions of this thesis can be summarized as follows:1. Having reviewed existing measurement matrixes, we propose a new method for construction of measurement matrix, which is based on engenvalue decomposition. In this method, we perform eigenvalue decomposition over the covariance matrix of Gaussian random matrix and use the maxtrix composed of eigenvalues as the measurement matrix in CS. The performance of the constructed matrix is verified and compared to that of a number of existing measurement matrixes via simulations. The simulation results suggest that:(1) The constructed matrix retains the RIP property of random Gaussian matrix and approaches the idea Gaussian matrix interms of reconstruction precision;(2) In comparison with quasi-Toeplitz matrix, Generalized Rotation matrix and QR-based matrix, our proposed matrix shows better performance in terms of matching degree of the original signal and the reconstruction signal and reconstruction precision;(3) Nevertheless, the implementation complexity introduced by the engen decomposition increase the time consumption to some extent.2. From the perspective of energy capture, we study the sparse approximation of UWB signals and propose a redundant dictionary reconstruction method based on the eigenvectors. The key idea is to calculate the covariance matrix of UWB signals based on the channel model, and then engenvectors are obtained by performing engen decomposition. The engenvectors are finally used to construct redundant dictionary for use in signal reconstruction. Due to the fact that most energy of UWB signals lies in a small collection of engen vectors statistically, the constructed dictionary is capable of improving the signal sparsity, reducing the sampling rate and boosting the efficiency of the signal reconstruction. The performance of the proposed scheme in typical UWB channels is analyzed and compared with that of existing redundant dictionaries via simulations. The simulation results suggest that:(1) For given scale of measurement matrix and number of reconstruction iterations, the engenvectors-based redundant dictionary outperforms its counterparts based on time sparsity and/or multipath sparsity in terms of reconstruction precision;(2) If the reconstructed template is employed by UWB receivers, the detection performance achieved by the engenvectors-based redundant dictionary is remarkably superior to that achieved by its counterparts, e.g., when BER is10-2, a SNR gain more than5dB can be observed in CM1channels;(3) The engenvectors-based redundant dictionary shows efficient energy capture with lowered number of measurements, e.g., when the number of measurements is25,80%of the signal energy can be captured in CM1channels.